Commutative Ring, Subgroups, Subrings, Ideals

Let be the set of functions . Given that forms a commutative ring with indentity under (pointwise) addition and multiplication,

(a) Find a subgroup of which is not a subring. Why?
(b) Find a subring of which is not an ideal. Why?
(c) Find an ideal of which is not the zero ring or . Can this ideal be written as a principal idea? Why?